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Alan
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Re: Philosophy of Mathematics

December 17th, 2021, 4:35 pm

square root of probability any interpretation? 
In quantum mechanics, it's (roughly) the wave function: [$]|\psi(x)|^2 dx = p(x) \, dx[$], where [$]p(x)[$] is a pdf. 
 
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Collector
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Re: Philosophy of Mathematics

December 17th, 2021, 7:20 pm

square root of probability any interpretation? 
In quantum mechanics, it's (roughly) the wave function: [$]|\psi(x)|^2 dx = p(x) \, dx[$], where [$]p(x)[$] is a pdf. 
unfortunately these probabilities are not satisfactory, not even according to Prince Louis-Victor Pierre Raymond de Broglie :
He lived long and kept a sharp mind, the French wine?
 
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Marsden
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Re: Philosophy of Mathematics

December 18th, 2021, 2:45 pm

Probability is just a number, the units cancel out: two beans red out of ten beans total means 20% probability of picking a red bean.

But there's no beans about the 20%.

So the square root of probability is just a number, too.
 
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bearish
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Joined: February 3rd, 2011, 2:19 pm

Re: Philosophy of Mathematics

December 18th, 2021, 6:07 pm

If you know that the probability of the joint occurrence of two iid random variables is p, then [$] \sqrt{p} [$] is the probability of the occurrence of each.
 
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trackstar
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Joined: January 1st, 1970, 12:00 am

Re: Philosophy of Mathematics

January 28th, 2022, 2:47 am

Found this book in a university ghost town a few days ago - empty streets, but plenty of coffee and books available in the stores that were open.

Synthetic Philosophy of Contemporary Mathematics - Fernando Zalamea

From one of the reviews: "Three different approaches to Mathematics are outlined, which the author calls eidal (transfusions of form: very much pure Mathematics, including mathematics of mathematics), quiddital (transfusions of the real, mathematics based in physics), and archaeal (decantations of the Universal)."

 So far, reminiscent of Badiou. If you read and enjoyed The Blank Swan (Elie Ayache), this is worth a look.
 
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Marsden
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Re: Philosophy of Mathematics

January 28th, 2022, 5:55 pm

"eidal ... quiddital ... and archaeal."
Also second year courses at Hogwarts, if I'm not mistaken ...